Tsai's Father, Dr. Paul C. Tsai, a native of Huzhou in Zhejiang, China, was born and grew up in Shanghai and moved to Taiwan in 1948. He came to Yale in 1953, received a LL.M. degree in 1954, and in 1957 became the first ever from Taiwan to receive a J.S.D. degree from Yale Law. Upon graduation, he returned to Taiwan, served in various key government roles for 8 years, and played a leading role in drafting policies and laws that contributed to Taiwan’s economic miracle and integration into the international economy. In 1965, he turned to private practice and with his Father, Ruchin Tsar (Chinese: 蔡六乘, born Jan 2, 1903 in Shanghai and died 1993), founded Taiwan’s first partnership law firm Tsar & Tsai, an industry pioneer with a reputation for quality and innovation, which also contributed greatly to Taiwan’s growth and development, particularly in the international arena by representing multinational corporations to attract foreign capital to Taiwan.

Tsai became as a tax associate at Sullivan & Cromwell right after graduation and was admitted in New York on May 6, 1991. After three years at the law firm, he switched to private equity and joined Rosecliff, Inc., a small management buyout firm based in New York, as vice President and general counsel, seeking a role that allowed him to make decisions instead of advices. He left for Hong Kong in 1995 to join Investor AB, where he was responsible for its Asian private equity Investments.

It was in this role that he first met Jack Ma in 1999 in Hangzhou after being introduced by a friend who was trying to sell his own company to Ma. Tsai was impressed with Ma’s idea to create an international import and export marketplace, as well as his charismatic personality, but it was Ma's followers and their Energy and enthusiasm that ultimately convinced Tsai. Later that year he quit the $700,000-a-year job at Investor AB and offered to join Ma as a member of the founding team for almost nothing. At the time each of Alibaba’s 18 co-founders—of which Tsai was the only Western-educated member—accepted a salary of only $600 a year. He served as chief operating officer, chief financial officer, and founding board member. He single-handedly established Alibaba's financial and legal structure, since no other member of the team had any experience in venture capital or law. In May 2013, he became Alibaba's executive vice chairman. Due to his unique contribution, he has become the second-largest individual shareholder of Ali Baba, right after Ma.

Joseph Tsai was born in Taipei, Taiwan to Dr. Paul C. Tsai (Chinese: 蔡中曾, died May 4, 2013), a second-generation Lawyer, and his wife Ruby. He has three younger siblings, Eva, Vivian, and Benjamin. At age 13, Tsai was sent by his parents to the Lawrenceville School, where he played lacrosse and was a member of the Cleve House. Tsai enrolled in his father's alma mater, Yale University, and played lacrosse there as well. He received a bachelor of arts' degree in economics and East Asian studies from Yale College in 1986, and a juris Doctor degree from Yale Law School in 1990.

On December 1, 2016, Yale announced a university-wide project center for innovative thinking with a mission to inspire students from diverse backgrounds and disciplines to seek innovative ways to solve real-world problems. Six months later, in May 2017, Tsai and his wife, through the Joe and Clara Tsai Foundation, made another donation to Yale for the construction, launch, and programs of the center and named it Tsai Center for Innovative Thinking.

One month later, in June 2017, Tsai and his wife, again through the Joe & Clara Tsai Foundation, made a donation to his high school, the Lawrenceville School, which was the single largest gift the school ever received. Tsai is a member of Lawrenceville's board of trustees.